Centrality-dependence of direct photon production
from Au+Au Collisions
QM2009 Knoxville, March 30 - April 4, 2009
F.M. Liu Central China Normal University, China
T. Hirano University of Tokyo, Japan
K. Werner University of Nantes, France
Y. Zhu Central China Normal University, China
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Outline
• Motivations• Calculation approach• Results• Conclusion
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Motivations• The properties of the hot dense matter created in heavy ion collision are of great i
nterest, especially the critical behaviors.
• As penetrating probes, direct photons can provide the inner information of the ho
t dense matter.
• Theoretically, photon production can easily be studied both macroscopically and
microscopically, which may be helpful for the study of hadron production.
• What can we learn from direct photon observables? How is this sig
nal related to hadronic signal?
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Calculation approachA precise calculation requires careful treatments on
• The space-time evolution of the created hot dense matter
distributions of thermal partons and hadrons
• The propagation of jets in plasma
distribution of hard partons
• All sources of direct photons
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the evolution of the matter
),,,,...(,,,, zyxBsup
%) ,(d
dnParameters are constrained with PHOBOS data Tested with hadrons’ yields, spectra, v2 and particles correlation
For more details, read T. Hirano
3D ideal hydrodynamic equation
Initial condition: Glauber model,
EoS: QGP phase: 3 flavor free Q & G gas
HG phase: hadronic gas PCE
fm/c6.00 Described with
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Distribution of hard partons
)ˆˆˆ()(ˆ
ˆ),(),( 2
/2
/AB2
jet
utscdabtd
dsMxGMxGdxdxTK
pdyd
dNbBb
abcdaAaba
t
AB
),()()()( /// AxRxGA
ZxG
A
NxG EKS
apaNaAa
MRST 2001 LO pDIS and EKS98 nuclear modification are employed
)(),2
(),2
(),(30 zy
bxTy
bxT
pd
dNrpf BA
Jet phase space distribution at τ=0:
)(),(),,(),( 00003 Evpptvrpfpdrpfxpf
at τ>0:
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Parton Energy Loss in a Plasma
• Energy loss of parton i=q, g,
• Energy loss per unit distance, i,e, with BDMPS
D: free parameter
• Every factor depends on the location of jet in plasma , i.e.,
0
))(,())(,,( ),,( 00 rfridrpiE QGP
is EDri / ))(,,( *2
)/8ln()233(
6)(
cfs TTN
T
upE *
)(r
fQGP: fraction of QGP at a given point
8
Fix D with pi0 suppression
A common D=1.5for various Centralities!
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Sources of direct photons• Leading Order contr. from primordial NN scatterings
• Thermal contribution
upETExd
pdyd
dN
t
**thermal
42
thermal
),,(
qqg
gqq
)ˆˆˆ()(ˆ
ˆ),(),( 2
/2
/AB2
)LO(
utscdabtd
dsMxGMxGdxdxT
pdyd
dNbBb
abaAaba
t
AB
2004 al,et Rapp R.
1991 al,et Kapusta:),( *HG TE
AMY/
22
*QGP
1
1
2
)(
9
6),( * C
eT
TTE
TEs
Interactions of thermal partonsare inside the rate!
Coupling depends on temperature
...effect LPM
qqg
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Sources of direct photons• Jet photon conversion
• Fragmentation contribution:
Sources not included: Medium induced Bremsstrahlung
Radiation from pre-equilibrium phase
qqg
gqq
C
Tg
TETxpfeTE q
S22
*22
2*
JPC
24ln),(
4),(
),( *JPC
42
TExdpdyd
dN
t
JPC
),(1 20
/2t
2,t
2QzD
zpdyd
dNdz
pdyd
dNcc
c
c
gqcc
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Results
• pt-spectra
• Elliptic flow (at low pt)
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pt-spectra
The measured pt spectrum is reproduced with 4 sources.Jet quenching plays a role but not so evident here.
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Direct photons are not suppressed?Reason: Due to the dominance of leading order contribution.
Consequence:The high pt elliptic flow mightbe too small to be visible.
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jet quenching effect at high pt
• Jet quenching treatment is very important in fragmentation contribution
and jet photon-conversion contribution.
• If one can separate the different sources via particle correlations,
then high pt suppression and v2 caused by jet quenching and by
geometry may be observed!
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V2 of thermal photons
• In the local rest frame, photons are emitted from the thermal bath isotropically.
• Thermal photons’ v2 is caused by the Lorentz boost and accumulated with the space-time integration.
• Both the strength and the asymmetry of the transverse flow are important.
upETExd
pdyd
dN
t
**thermal
42
thermal
),,( dominant source at low pt.
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Time evolution of the transverse flow
22
22
222
yx
yxHyxr vv
vvvvvv
Energy-weighted Space-averaged
Transverse flow gets stronger with time.
The asymmetry increases with eccentricity.
22
22
222
yx
yxHyxr vv
vvvvvv
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thermal photons v2 time evolution
Elliptic flow of thermal photons decreases at high pt due to the abundant emission at early time.
Fraction emitted at earlier timeIncreases with pt.
Elliptic flow of thermal photonsincreases with time.
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V2(pt) at different centrality
Elliptic flow of thermal photons does decrease at high pt.
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Centrality dependence of pt-int. v2
Maximum pt-int. v2 appears at 40-50% centrality, due to the interplay between the strength and asymmetry of the transverse flow.
This centrality dependence is similar to the measured hadronic v2.
The measurement of elliptic flow of thermal photons( direct photons) is really needed to test models!
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QGP phase and HG phase
V2 from hadronic phase is much bigger than from QGP phase.
V2 can carry different information than pt spectrum.
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Dependence of EoS?
Elliptic flow is more sensitive to EoS than pt spectrum!
Various input of EoS
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Conclusion• Ideal hydro model can reproduce the measured pt spectra of direct photo
ns at different centrality with the four sources we considered.
• Jet quenching plays a role in direct photon production.
• pt-int. v2 reaches maximum at 40-50% centrality, due to the interplay bet
ween the strength and asymmetry of the transverse flow.
Does this interplay play a role in hadronic elliptic flow? How?
• Thermal photon V2 is more sensitive to EoS than pt spectra!
• Measurement is needed to test the model.
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Thank you!
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Isosping mixture and nuclear shadowing:
RAA suppression from initial effect
),()]()(
)([)( /// AxRxGA
zAxG
A
zxG EKS
aNapaAa
)ˆˆˆ()(ˆ
ˆ),(),( 2
/2
/AB2
)LO(
utscdabtd
dsMxGMxGdxdxT
pdyd
dNbBb
abaAaba
t
AB
The dominant contribution at high pt is the LO contribution from NN collisions:
The isospin mixtureand nuclear shadowing reduce Raa at high pt.
This is the initial effect, not related to QGP formation.
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Fix D with pi0 suppression • From pp collisions:
• From AA collisions, parton energy loss is considered
via modified fragmentation function
),(1 20
/2t
2,t
2
0
QzDzpdyd
dNdz
pdyd
dNcc
c
cpp
gqcc
pp
Factorization scale and renormalization scale to be tpQM
functionion fragmentat KKP :),( 20/ QzD cc
),,( 2/ ccc EQzD X.N.Wang’s formula
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Why jets lose energy
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Pt spectrum from pp collisionsPRL 98, 012002 (2007)
A good test for contributions from leading order +fragmentation without Elossin AA collisions.
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Thermal fraction
